Espargaro was taken to hospital for scans on his right hand and abdomen on Saturday after he sent flying from his GSX-RR in a huge high-side accident.
The Spaniard was cleared to take part in qualifying later that day and posted the 10th fastest time, only for his race to end after just two laps due to clutch failure.
The 25-year-old was examined by surgeon Dr Xavier Mir on Monday and it was decided that surgery was the best course of action to repair the ligament damage that Espargaro had suffered.
"Aleix suffered a rupture in the ulnar collateral ligament of the metacarpophalangeal joint of the right thumb, confirmed by ultrasound and x-rays," said Dr Mir.
"This injury causes joint instability and therefore a surgical repair is necessary."
Espargaro is expected to be fit feature at Italian GP at Mugello on May 31.